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Use thermal analysis to predict an IC's transient behavior and avoid overheating

• TB1 = T1em1t + T2em2t + T3em3t + TA + (θ12 + θ23 + θ3A)PG

  (Eq. 21)

  
  

  Where:
  θ12 is the thermal resistance from Body 1 to Body 2.
  θ23 is the thermal resistance from Body 2 to Body 3.
  θ3A is the thermal resistance from Body 3 to the environment.
  T1, T2, and T3 are the constants of integration.
  m1, m2, and m3 are functions of k1, k2, and k3.
  
  Equation 21 predict电感单位s die temperature in a very accurate way when the die is generating power. To use this equation, however, we must know all the constants of integration plus m1, m2, and m3, which are complicated functions whose solution is difficult. To avoid this difficult exercise, we use a tool for solving differential equations: SPICE.
  
  

  RC network models thermal-transient differential equations

  We will now propose a circuit modeled by similar differential equations, and we will then simulate the circuit and read out temperatures from the simulation.
  
  The differential Equations 18, 19, and 20 can be modeled by a simple RC network (F塑封电感igure 4) that represents the power generated on the die.
  
  
  Figure 4. This RC network models the transient-thermal behavior of a chip when heat is generated internally.
  
  In Figure 4 initial voltages on the capacitors represent the initial temperatures of the die (C1), the epoxy (C2), and the package (C3). VA represents the ambient temperature of the environment, and IS (the current going into capacitor C1) represents the power generated on the die. The differential equations representing voltages on the capacitors are:

  (Eq. 22)

  
  

  (Eq. 23)

  
  

  (Eq. 24)

  
  

  These three equations correspond to Equations 18, 19, and 20, with the following substitutions of variables:
  
  VC1 TB1, VC2 TB2, VC3 TB3, lS PG
  
  The capacitor voltages correspond directly to the temperatures of the die, epoxy, and package. Any SPICE package can simulate the RC circuit easily. When we know the proper values of R1, R2, R3, C1, C2, and C3 modeled for a particular chip, we can then simulate the circuit and directly read out die temperature as the voltage on capacitor C1.
  
  Now we can determine the passive component values for a particular chip (R1, R2, R3, C1, C2, and C3). Use Equation 5 (repeated below as Equation 25) to obtain the thermal resistance for the system (θJA) by measuring the die's steady-state final temperature:

  (Eq. 25)

  
  

  Where:
  TJ is the steady-state junction temperature of the die.
  TA is the ambient temperature.
  PG is the power dissipated on the die.
  
  Operating with the same dissipated power (PG) as in Equation 25, you can create a data set for the chip's transient temperature variation by measuring the die temperature at different times starting at time 0. Then, based on the following constraint, do a curve-fitting exercise on the measured data to determine the values of R1, R2, R3, C1, C2, and C3:
  
  

  θJA = R1 + R2 + R3

  (Eq. 26)

  
  

  Measuring the die temperature

  There are a couple of practical methods to measure the die temperature of an integrated circuit.3 Here we will use the ESD diode forward-drop measurem电感器工作原理ent method to determine the chip temperature, since it is easy and will not introduce a large amount of error. However, to ensure that the accuracy levels of the measurement remain within acceptable limits, always choose the die-temperature measurement technique for a particular chip carefully. The following guidelines will prove helpful.3

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